306 



SCIENCE. 



[X. S. Vol. XXI. Xo. 530. 



portions of matter. One of the most common 

 and vicious errors is that action and reaction 

 are counterbalancing forces. This error will 

 inevitably be made if stress is defined as ac- 

 tion and reaction, and then used to designate 

 a pair of counterbalancing forces. Professor 

 Maurer's usage, while departing from both the 

 above definitions, is clear and consistent. He 

 defines stress as any force whose place of appli- 

 cation is a surface. 



Most present-day text-books, including the 

 three before us, define centrifugal force as the 

 reaction which a particle constrained to de- 

 scribe a curved path, or a rigid body con- 

 strained to rotate about a fixed axis, exerts 

 upon the constraining body. This definition 

 is clear, and would be satisfactory if it were 

 not inconsistent with general usage in the 

 only class of problems in which the term is 

 really needed — i. e., problems in which motion 

 is referred to rotating axes. It is convenient 

 in such cases to give the equation of motion 

 of a particle the same form as if the axes were 

 fixed, introducing such fictitious forces as 

 would produce the accelerations actually due 

 to the motion of the axes. One component 

 of the fictitious force for each particle is the 

 centrifugal force, which is thus not a reaction 

 exerted by the particle but a force assumed to 

 act upon it. This must be regarded as the 

 legitimate use of the term centrifugal force. 

 Inconsistency in the use of this term in ele- 

 mentary text-books is responsible for much 

 confusion in the mind of the student. An 

 example of this inconsistency occurs in 

 Stephan's book, pp. 279, 281. Centrifugal 

 force is defined as the reaction exerted by a 

 particle upon the body which deflects it from 

 a straight path. But in the discussion of the 

 belt and pulley an element of the belt is said 

 to ' experience ' a centrifugal force. 



So much confusion of thought has been 

 shown in discussions of ' inertia-force ' that it 

 seems desirable to drop the term entirely. 

 Those who use it often appeal to the authority 

 of Newton ; but it is well known that Newton 

 did not restrict the word force to its present 

 specialized meaning, and that which he meant 

 by force of inertia is not force at all in the 

 present meaning of the word. Professor 



Ziwct defines force of inertia of a particle as 

 the reversed effective force, i. e., a force — mj, 

 m being the mass of the particle and its 

 acceleration; and he explains that this force 

 is exerted not on the jjarticle but bj- it, being 

 the reaction to the force which acts upon the 

 panicle to produce its acceleration. A stu- 

 dent who compares this statement with the 

 following (p. 160) is likely to be somewhat 

 bewildered : " The fact that any change of mo- 

 tion in a physical body is affected by its mass 

 is sometimes ascribed to the so-called ' inertia,' 

 or ' force of inertia,' of matter, which means, 

 however, nothing else but the property of pos- 

 sessing mass." This latter statement is prac- 

 tically Newton's explanation of force of in- 

 ertia. 



The preceding definition (also given by 

 Stephan) is sanctioned by various writers of 

 high authority. It may, however, be doubted 

 whether there is any real need of a term to 

 designate the reversed effective force — mj; 

 at all events the term inertia-force used in 

 this sense seems inappropriate and misleading- 

 The nature of the action to which we give the 

 name force does not depend upon whether the 

 body exerting it has or has not acceleration. 

 Suppose, for example, that a particle is acted 

 upon by two bodies only, A exerting a force P 

 upon it and B a force Q, and let R be the 

 vector sum of P and Q. The particle reacts 

 ujion A with a force — P and upon B with a 

 force — Q ; there is no body upon which it 

 exerts a force — mj = — R. The ' inertia- 

 force ' is thus merely the vector sum of two 

 forces exerted by the particle upon different 

 bodies. There is nothing peculiar about these 

 forces, and no reason why either of them 

 should be attributed to the ' inertia ' of the 

 body. If P and Q become equal and opposite, 

 the so-called inertia-force becomes zero, but 

 the nature of the forces P and Q and of the 

 reactions to them is unchanged. Neither is 

 the nature of P or of its reaction changed if 

 Q ceases to act ; there is no more reason in this 

 case than in the preceding for attributing the 

 force exerted upon A to the inertia of the 

 particle. 



L. M. HosKixs. 



Stanford University. 



